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  Subjects -> ENGINEERING (Total: 2167 journals)
    - CHEMICAL ENGINEERING (184 journals)
    - CIVIL ENGINEERING (168 journals)
    - ELECTRICAL ENGINEERING (94 journals)
    - ENGINEERING (1173 journals)
    - ENGINEERING MECHANICS AND MATERIALS (355 journals)
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ENGINEERING (1173 journals)            First | 4 5 6 7 8 9 10 11 | Last

Journal of Industrial Engineering and Management     Open Access   (Followers: 4)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 1)
Journal of Inverse and Ill-posed Problems     Hybrid Journal   (Followers: 1)
Journal of Irrigation and Drainage Engineering     Full-text available via subscription   (Followers: 15)
Journal of K-Theory     Full-text available via subscription   (Followers: 1)
Journal of King Saud University - Engineering Sciences     Open Access  
Journal of Konbin     Open Access  
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 9)
Journal of Management in Engineering     Full-text available via subscription   (Followers: 11)
Journal of Manufacturing Science and Engineering     Full-text available via subscription   (Followers: 11)
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 6)
Journal of Manufacturing Technology Management     Hybrid Journal   (Followers: 4)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 2)
Journal of Mechatronics     Full-text available via subscription   (Followers: 1)
Journal of Membrane and Separation Technology     Hybrid Journal  
Journal of Metallurgy     Open Access   (Followers: 4)
Journal of Middle European Construction and Design of Cars     Open Access   (Followers: 1)
Journal of Molecular Catalysis B: Enzymatic     Hybrid Journal   (Followers: 1)
Journal of Motor Behavior     Hybrid Journal   (Followers: 9)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 7)
Journal of Nanoengineering and Nanomanufacturing     Full-text available via subscription   (Followers: 2)
Journal of Nanoparticle Research     Hybrid Journal   (Followers: 2)
Journal of Nanoscience     Open Access  
Journal of Nanoscience and Nanotechnology     Full-text available via subscription   (Followers: 13)
Journal of NanoScience, NanoEngineering & Applications     Full-text available via subscription  
Journal of Nanotechnology     Open Access   (Followers: 4)
Journal of Nanotechnology in Engineering and Medicine     Full-text available via subscription   (Followers: 7)
Journal of Natural Gas Science and Engineering     Hybrid Journal   (Followers: 3)
Journal of Near Infrared Spectroscopy     Full-text available via subscription   (Followers: 7)
Journal of Networks     Open Access   (Followers: 4)
Journal of Nonlinear Dynamics     Open Access  
Journal of Nuclear Engineering & Technology     Full-text available via subscription  
Journal of Ocean Engineering and Marine Energy     Hybrid Journal  
Journal of Oceanography and Marine Science     Open Access   (Followers: 2)
Journal of Operations Management     Hybrid Journal   (Followers: 19)
Journal of Optics     Hybrid Journal   (Followers: 3)
Journal of Optimization     Open Access  
Journal of Optoelectronics Engineering     Open Access  
Journal of Organizational Behavior     Hybrid Journal   (Followers: 35)
Journal of Petroleum Science Research     Open Access  
Journal of Phase Equilibria and Diffusion     Hybrid Journal   (Followers: 5)
Journal of Power Sources     Partially Free   (Followers: 31)
Journal of Pre-College Engineering Education Research     Open Access  
Journal of Pressure Vessel Technology     Full-text available via subscription   (Followers: 11)
Journal of Professional Issues in Engineering Education and Practice     Full-text available via subscription   (Followers: 6)
Journal of Quality and Reliability Engineering     Open Access   (Followers: 1)
Journal of Quality in Maintenance Engineering     Hybrid Journal   (Followers: 4)
Journal of Radiation Research and Applied Sciences     Open Access   (Followers: 1)
Journal of Rare Earths     Full-text available via subscription   (Followers: 2)
Journal of Real-Time Image Processing     Hybrid Journal   (Followers: 5)
Journal of Regional Science     Hybrid Journal   (Followers: 11)
Journal of Reinforced Plastics and Composites     Hybrid Journal   (Followers: 27)
Journal of Research of NIST     Open Access   (Followers: 1)
Journal of Research Updates in Polymer Science     Hybrid Journal  
Journal of Rock Mechanics and Geotechnical Engineering     Open Access   (Followers: 2)
Journal of Russian Laser Research     Hybrid Journal  
Journal of Safety Engineering     Open Access   (Followers: 6)
Journal of Safety Research     Hybrid Journal   (Followers: 21)
Journal of Science and Technology     Open Access  
Journal of Science and Technology (Ghana)     Open Access   (Followers: 2)
Journal of Science and Technology Policy Management     Hybrid Journal   (Followers: 2)
Journal of Scientific Computing     Hybrid Journal   (Followers: 3)
Journal of Scientific Innovations for Development     Open Access   (Followers: 2)
Journal of Semiconductors     Full-text available via subscription   (Followers: 2)
Journal of Sensor Technology     Open Access   (Followers: 3)
Journal of Shanghai Jiaotong University (Science)     Hybrid Journal  
Journal of Sol-Gel Science and Technology     Hybrid Journal   (Followers: 1)
Journal of Solar Energy     Open Access   (Followers: 5)
Journal of Solar Energy Engineering     Full-text available via subscription   (Followers: 16)
Journal of Superconductivity and Novel Magnetism     Partially Free   (Followers: 1)
Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques     Hybrid Journal   (Followers: 2)
Journal of Surveying Engineering     Full-text available via subscription   (Followers: 7)
Journal of Technology Management & Innovation     Open Access   (Followers: 4)
Journal of Testing and Evaluation     Full-text available via subscription   (Followers: 17)
Journal of the Air & Waste Management Association     Hybrid Journal   (Followers: 3)
Journal of the Chinese Institute of Engineers     Hybrid Journal  
Journal of the Chinese Institute of Industrial Engineers     Hybrid Journal   (Followers: 1)
Journal of the Franklin Institute     Full-text available via subscription  
Journal of the Institution of Engineers (India ): Series D     Hybrid Journal  
Journal of the Institution of Engineers (India) : Series B     Hybrid Journal   (Followers: 1)
Journal of The Institution of Engineers (India) : Series E     Hybrid Journal   (Followers: 1)
Journal of the Institution of Engineers (India): Series A     Hybrid Journal  
Journal of the Institution of Engineers (India): Series C     Hybrid Journal   (Followers: 1)
Journal of the National Science Foundation of Sri Lanka     Open Access   (Followers: 1)
Journal of the University of Ruhuna     Open Access  
Journal of Thermal Science and Engineering Applications     Full-text available via subscription   (Followers: 3)
Journal of Thermal Stresses     Hybrid Journal   (Followers: 3)
Journal of Transplantation     Open Access   (Followers: 4)
Journal of Transport and Supply Chain Management     Open Access   (Followers: 8)
Journal of Transportation Engineering     Full-text available via subscription   (Followers: 14)
Journal of Transportation Systems Engineering and Information Technology     Full-text available via subscription   (Followers: 14)
Journal of Tribology     Full-text available via subscription   (Followers: 27)
Journal of Turbomachinery     Full-text available via subscription   (Followers: 10)
Journal of Turbulence     Hybrid Journal   (Followers: 1)
Journal of Unmanned Vehicle Systems     Full-text available via subscription   (Followers: 2)
Journal of Urban and Environmental Engineering     Open Access   (Followers: 1)
Journal of Urban Planning and Development     Full-text available via subscription   (Followers: 33)
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 17)
Journal of Vibration and Acoustics     Full-text available via subscription   (Followers: 29)

  First | 4 5 6 7 8 9 10 11 | Last

Journal Cover   Physica D: Nonlinear Phenomena
  [SJR: 1.048]   [H-I: 89]   [3 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0167-2789
   Published by Elsevier Homepage  [2800 journals]
  • Editorial Board
    • Abstract: Publication date: 1 August 2015
      Source:Physica D: Nonlinear Phenomena, Volume 309




      PubDate: 2015-08-31T19:27:50Z
       
  • Numerical and experimental observation of Arnol’d resonance webs in
           an electrical circuit
    • Abstract: Publication date: Available online 31 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Naohiko Inaba, Kyohei Kamiyama, Takuji Kousaka, Tetsuro Endo
      An extensive bifurcation analysis of partial and complete synchronizations of three-frequency quasi-periodic oscillations generated in an electric circuit is presented. Our model uses two-coupled hysteresis oscillators and a rectangular wave forcing term. The governing equation of the circuit is represented by a piecewise-constant dynamics generating a three-dimensional torus. The Lyapunov exponents are precisely calculated using explicit solutions without numerically solving any implicit equation. By analyzing this extremely simple circuit, we clearly demonstrate that it generates an extremely complex bifurcation structure called Arnol’d resonance web. Inevitably, chaos is observed in the neighborhood of Chenciner bubbles around which regions generating three-dimensional tori emanate. Furthermore, the numerical results are experimentally verified.


      PubDate: 2015-08-31T19:27:50Z
       
  • KAM tori and whiskered invariant tori for non-autonomous systems
    • Abstract: Publication date: Available online 20 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Marta Canadell, Rafael de la Llave
      We consider non-autonomous dynamical systems which converge to autonomous (or periodic) systems exponentially fast in time. Such systems appear naturally as models of many physical processes affected by external pulses. We introduce definitions of non-autonomous invariant tori and non-autonomous whiskered tori and their invariant manifolds and we prove their persistence under small perturbations, smooth dependence on parameters and several geometric properties (if the systems are Hamiltonian, the tori are Lagrangian manifolds). We note that such definitions are problematic for general time-dependent systems, but we show that they are unambiguous for systems converging exponentially fast to autonomous. The proof of persistence relies only on a standard implicit function theorem in Banach spaces and it does not require that the rotations in the tori are Diophantine nor that the systems we consider preserve any geometric structure. We only require that the autonomous system preserves these objects. In particular, when the autonomous system is integrable, we obtain the persistence of tori with rational rotational. We also discuss fast and efficient algorithms for their computation. The method also applies to infinite dimensional systems which define a good evolution, e.g. PDE’s. When the systems considered are Hamiltonian, we show that the time dependent invariant tori are isotropic. Hence, the invariant tori of maximal dimension are Lagrangian manifolds. We also obtain that the (un)stable manifolds of whiskered tori are Lagrangian manifolds. We also include a comparison with the more global theory developed in Blazevski and de la Llave (2011).


      PubDate: 2015-08-23T09:51:06Z
       
  • Stabilty of heteroclinic cycles in transverse bifurcations
    • Abstract: Publication date: Available online 20 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Alexander Lohse
      Heteroclinic cycles and networks exist robustly in dynamical systems with symmetry. They can be asymptotically stable, and gradually lose this stability through a variety of bifurcations, displaying different forms of non-asymptotic stability along the way. We analyse the stability change in a transverse bifurcation for different types of simple cycles in R 4 . This is done by first showing how stability of the cycle or network as a whole is related to stability indices along its connections — in particular, essential asymptotic stability is equivalent to all local stability indices being positive. Then we study the change of the stability indices. We find that all cycles of types B and C are generically essentially asymptotically stable after a transverse bifurcation, and that no type B cycle can be almost completely unstable (unlike type C cycles).


      PubDate: 2015-08-23T09:51:06Z
       
  • Simple analytic approximations for the Blasius problem
    • Abstract: Publication date: Available online 13 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): R. Iacono, John P. Boyd
      The classical boundary layer problem formulated by Heinrich Blasius more than a century ago is revisited, with the purpose of deriving simple and accurate analytical approximations to its solution. This is achieved through the combined use of a generalized Padé approach and of an integral iteration scheme deviced by Hermann Weyl. The iteration scheme is also used to derive very accurate bounds for the value of the second derivative of the Blasius function at the origin, which plays a crucial role in this problem.


      PubDate: 2015-08-15T04:48:40Z
       
  • Cellular non-deterministic automata and partial differential equations
    • Abstract: Publication date: Available online 11 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): D. Kohler, J. Müller, U. Wever
      We define cellular non-deterministic automata (CNDA) in the spirit of non-deterministic automata theory. They are different from the well-known stochastic automata. We propose the concept of deterministic superautomata to analyze the dynamical behavior of a CNDA and show especially that a CNDA can be embedded in a deterministic cellular automaton. As an application we discuss a connection between certain partial differential equations and CNDA.


      PubDate: 2015-08-15T04:48:40Z
       
  • Variational integrators for nonvariational partial differential equations
    • Abstract: Publication date: Available online 13 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Michael Kraus, Omar Maj
      Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian via Noether’s theorem. An inevitable prerequisite for the derivation of variational integrators is the existence of a variational formulation for the considered problem. Even though for a large class of systems this requirement is fulfilled, there are many interesting examples which do not belong to this class, e.g., equations of advection-diffusion type frequently encountered in fluid dynamics or plasma physics. On the other hand, it is always possible to embed an arbitrary dynamical system into a larger Lagrangian system using the method of formal (or adjoint) Lagrangians. We investigate the application of the variational integrator method to formal Lagrangians, and thereby extend the application domain of variational integrators to include potentially all dynamical systems. The theory is supported by physically relevant examples, such as the advection equation and the vorticity equation, and numerically verified. Remarkably, the integrator for the vorticity equation combines Arakawa’s discretization of the Poisson brackets with a symplectic time stepping scheme in a fully covariant way such that the discrete energy is exactly preserved. In the presentation of the results, we try to make the geometric framework of variational integrators accessible to non specialists.


      PubDate: 2015-08-15T04:48:40Z
       
  • Editorial Board
    • Abstract: Publication date: 15 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 308




      PubDate: 2015-08-10T04:29:17Z
       
  • Blow up criterion of strong solution for 3D viscous liquid–gas
           two-phase flow model with vacuum
    • Abstract: Publication date: 1 August 2015
      Source:Physica D: Nonlinear Phenomena, Volume 309
      Author(s): Lili Du, Qin Zhang
      In this paper, we establish a blow-up criterion to the local strong solution to the three dimensional (3D) viscous liquid–gas two-phase flow model only in terms of the divergence of the velocity field. Moreover, the initial vacuum is allowed, and there is no extra restriction on viscous coefficients. Both the Cauchy problem and initial-boundary value problem are considered in this paper.


      PubDate: 2015-08-10T04:29:17Z
       
  • Derivation of a wave kinetic equation from the resonant-averaged
           stochastic NLS equation
    • Abstract: Publication date: 1 August 2015
      Source:Physica D: Nonlinear Phenomena, Volume 309
      Author(s): Sergei Kuksin, Alberto Maiocchi
      We suggest a new derivation of a wave kinetic equation for the spectrum of the weakly nonlinear Schrödinger equation with stochastic forcing. The kinetic equation is obtained as a result of a double limiting procedure. Firstly, we consider the equation on a finite box with periodic boundary conditions and send the size of the nonlinearity and of the forcing to zero, while the time is correspondingly rescaled; then, the size of the box is sent to infinity (with a suitable rescaling of the solution). We report here the results of the first limiting procedure, analysed with full rigour in Kuksin and Maiocchi (0000), and show how the second limit leads to a kinetic equation for the spectrum, if some further hypotheses (commonly employed in the weak turbulence theory) are accepted. Finally we show how to derive from these equations the Kolmogorov–Zakharov spectra.


      PubDate: 2015-08-10T04:29:17Z
       
  • Equivariant Hopf bifurcation with general pressure laws
    • Abstract: Publication date: Available online 6 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Tong Li, Jinghua Yao
      The equivariant Hopf bifurcation dynamics of a class of system of partial differential equations is studied. The connections between the current dynamics and fundamental concepts in hyperbolic conservation laws are explained. The unique approximation property of center manifold reduction function is used in the current work to determine certain parameter in the normal form. The current work generalizes the study of the second author (J. Yao, 2014) and discovers a class of examples of O ( 2 ) Hopf bifurcation with two parameters arising from systems of partial differential equations.


      PubDate: 2015-08-10T04:29:17Z
       
  • The scattering transform for the Benjamin–Ono equation in the
           small-dispersion limit
    • Abstract: Publication date: Available online 6 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Peter D. Miller, Alfredo N. Wetzel
      Using exact formulae for the scattering data of the Benjamin–Ono equation valid for general rational potentials recently obtained in Miller and Wetzel (2015), we rigorously analyze the scattering data in the small-dispersion limit. In particular, we deduce precise asymptotic formulae for the reflection coefficient, the location of the eigenvalues and their density, and the asymptotic dependence of the phase constant (associated with each eigenvalue) on the eigenvalue itself. Our results give direct confirmation of conjectures in the literature that have been partly justified by means of inverse scattering, and they also provide new details not previously reported in the literature.


      PubDate: 2015-08-10T04:29:17Z
       
  • A computational study of residual KPP front speeds in time-periodic
           cellular flows in the small diffusion limit
    • Abstract: Publication date: Available online 7 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Penghe Zu, Long Chen, Jack Xin
      The minimal speeds ( c ∗ ) of the Kolmogorov-Petrovsky-Piskunov (KPP) fronts at small diffusion ( ϵ ≪ 1 ) in a class of time-periodic cellular flows with chaotic streamlines is investigated in this paper. The variational principle of c ∗ reduces the computation to that of a principle eigenvalue problem on a periodic domain of a linear advection-diffusion operator with space-time periodic coefficients and small diffusion. To solve the advection dominated time-dependent eigenvalue problem efficiently over large time, a combination of spectral methods and finite element, as well as the associated fast solvers, are utilized to accelerate computation. In contrast to the scaling c ∗ = O ( ϵ 1 / 4 ) in steady cellular flows, a new relation c ∗ = O ( 1 ) as ϵ ≪ 1 is revealed in the time-periodic cellular flows due to the presence of chaotic streamlines. Residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub-diffusion process.


      PubDate: 2015-08-10T04:29:17Z
       
  • A geometric singular perturbation approach for planar stationary shock
           waves
    • Abstract: Publication date: Available online 5 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Zhuopu Wang, Jiazhong Zhang, Junheng Ren, Muhammad Nauman Aslam
      The non-linear non-equilibrium nature of shock waves in gas dynamics is investigated for the planar case. Along each streamline, the Euler equations with non-equilibrium pressure are reduced to a set of ordinary differential equations defining a slow-fast system, and geometric singular perturbation theory is applied. The proposed theory shows that an orbit on the slow manifold corresponds to the smooth part of the solution to the Euler equation, where non-equilibrium effects are negligible; and a relaxation motion from the unsteady to the steady branch of the slow manifold corresponds to a shock wave, where the flow relaxes from non-equilibrium to equilibrium. Recognizing the shock wave as a fast motion is found to be especially useful for shock wave detection when post-processing experimental measured or numerical calculated flow fields. Various existing shock detection methods can be derived from the proposed theory in a rigorous mathematical manner. The proposed theory provides a new shock detection method based on its non-linear non-equilibrium nature, and may also serve as the theoretical foundation for many popular shock wave detection techniques.


      PubDate: 2015-08-06T04:10:21Z
       
  • Averaging and spectral properties for the 2D advection-diffusion equation
           in the semi-classical limit for vanishing diffusivity
    • Abstract: Publication date: Available online 3 August 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): J. Vukadinovic, E. Dedits, A.C. Poje, T. Schäfer
      We consider the two-dimensional advection-diffusion equation on a bounded domain subject to Dirichlet or von Neumann boundary conditions involving a Liouville integrable Hamiltonian. Transformation to action-angle coordinates permits averaging in time and angle, resulting in an equation that allows for separation of variables. The Fourier transform in the angle coordinate transforms the equation into an effective diffusive equation and a countable family of non-self-adjoint Schrödinger equations. For the corresponding Liouville–Sturm problem, we apply complex-plane WKB methods to study the spectrum in the semi-classical limit for vanishing diffusivity. The spectral limit graph is found to consist of analytic curves (branches) related to Stokes graphs forming a tree-structure. Eigenvalues in the neighborhood of branches emanating from the imaginary axis are subject to various sublinear power laws with respect to diffusivity, leading to convection-enhanced rates of dissipation of the corresponding modes. The solution of ADE converges in the limit of vanishing diffusivity to the solution of the effective diffusion equation on convective time scales that are sublinear with respect to the diffusive time scales.


      PubDate: 2015-08-06T04:10:21Z
       
  • A computational overview of the solution space of the imaginary
           Painlevé II equation
    • Abstract: Publication date: Available online 30 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Bengt Fornberg, J.A.C. Weideman
      The six Painlevé equations were first formulated about a century ago. Since the 1970’s, it has become increasingly recognized that they play a fundamental role in a wide range of physical applications. A recently developed numerical pole field solver (Fornberg and Weideman, 2011) now allows their complete solutions spaces to be surveyed across the complex plane. Following such surveys of the P I , P I I and P I V equations, we consider here the case of the imaginary P I I equation (the standard P I I equation, with a change of sign for its nonlinear term). Solutions to this equation share many features with other classes of Painlevé transcendents, including a rich variety of pole field configurations, with connection formulas linking asymptotic behaviors in different directions of the complex plane.
      Graphical abstract image

      PubDate: 2015-08-02T03:25:09Z
       
  • Maxwell’s conjecture on three point charges with equal magnitudes
    • Abstract: Publication date: Available online 30 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Ya-Lun Tsai
      Maxwell’s conjecture on three point charges states that the number of non-degenerate equilibrium points of the electrostatic field generated by them in R 3 is at most four. We prove the conjecture in the cases when three point charges have equal magnitudes and show the number of isolated equilibrium points can only be zero, two, three, or four. Specifically, fixing positions of two positive charges in R 3 , we know exactly where to place the third positive charge to have two, three, or four equilibrium points. All equilibrium points are isolated and there are no other possibilities for the number of isolated equilibrium points. On the other hand, if both two of the fixed charges have negative charge values, there are always two equilibrium points except when the third positive charge lies in the line segment connecting the two negative charges. The exception cases are when the field contains only a curve of equilibrium points. In this paper, computations assisted by computer involve symbolic and exact integer computations. Therefore, all the results are proved rigorously.


      PubDate: 2015-08-02T03:25:09Z
       
  • The Whitham Equation as a model for surface water waves
    • Abstract: Publication date: Available online 31 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Daulet Moldabayev, Henrik Kalisch, Denys Dutykh
      The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of the water wave problem, it is thought to provide a more faithful description of shorter waves of small amplitude than traditional long wave models such as the KdV equation. In this work, we identify a scaling regime in which the Whitham equation can be derived from the Hamiltonian theory of surface water waves. The Whitham equation is integrated numerically, and it is shown that the equation gives a close approximation of inviscid free surface dynamics as described by the Euler equations. The performance of the Whitham equation as a model for free surface dynamics is also compared to different free surface models: the KdV equation, the BBM equation, and the Padé (2,2) model. It is found that in a wide parameter range of amplitudes and wavelengths, the Whitham equation performs on par with or better than the three considered models.


      PubDate: 2015-08-02T03:25:09Z
       
  • Global modes in nonlinear non-normal evolutionary models: Exact solutions,
           perturbation theory, direct numerical simulation, and chaos
    • Abstract: Publication date: Available online 26 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): LennonÓ. Náraigh
      This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal nonlinear system that not only highlights the phenomena of linear transient growth, subcritical transition and global modes, but is also of potential interest in its own right in the field of nonlinear optics. The second is the fairly familiar inhomogeneous nonlinear complex Ginzburg–Landau (CGL) equation. The two-level model is exactly solvable for the nonlinear global mode and its stability, while for the spatially-extended CGL equation, perturbative solutions for the global mode and its stability are presented, valid for inhomogeneities with arbitrary scales of spatial variation and global modes of small amplitude, corresponding to a scenario near criticality. For other scenarios, a numerical iterative nonlinear eigenvalue technique is preferred. Two global modes of different amplitudes are revealed in the numerical approach. For both the two-level system and the nonlinear CGL equation, the analytical calculations are supplemented with direct numerical simulation, thus showing the fate of unstable global modes. For the two-level model this results in unbounded growth of the full nonlinear equations. For the spatially-extended CGL model in the subcritical regime, the global mode of larger amplitude exhibits a ‘one-sided’ instability leading to a chaotic dynamics, while the global mode of smaller amplitude is always unstable (theory confirms this). However, advection can stabilize the mode of larger amplitude.


      PubDate: 2015-07-28T20:53:41Z
       
  • Detecting changes in coupling with Granger causality method from time
           series with fast transient processes
    • Abstract: Publication date: Available online 26 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Ilya V. Sysoev, Marina V. Sysoeva
      The ability of the Granger causality method to detect directed coupling between subsystems of a complex system in a moving time window is investigated on etalon oscillators. In particular, the time series consisting of alternate stationary regimes characterised by the different amplitude and shape of oscillations with fast transient processes between these regimes are considered, with similar transitions being possible due to changes either in the coupling or in the individual properties of subsystems. Two popular approaches to surrogate times series generation are used to check the significance of the method results. Two model structures: the standard linear and the special non-linear adapted to data are implemented. The Granger causality method using the model structure adapted to data is shown to be significantly advantageous in detecting coupling directionality and the instant time of the regime change than the standard linear method, while in some cases the sensitivity and the specificity of the adapted approach are insufficient.


      PubDate: 2015-07-28T20:53:41Z
       
  • Low-frequency variability and heat transport in a low-order nonlinear
           coupled ocean-atmosphere model
    • Abstract: Publication date: Available online 28 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Stéphane Vannitsem, Jonathan Demaeyer, Lesley De Cruz, Michael Ghil
      We formulate and study a low-order nonlinear coupled ocean–atmosphere model with an emphasis on the impact of radiative and heat fluxes and of the frictional coupling between the two components. This model version extends a previous 24-variable version by adding a dynamical equation for the passive advection of temperature in the ocean, together with an energy balance model. The bifurcation analysis and the numerical integration of the model reveal the presence of low-frequency variability (LFV) concentrated on and near a long-periodic, attracting orbit. This orbit combines atmospheric and oceanic modes, and it arises for large values of the meridional gradient of radiative input and of frictional coupling. Chaotic behavior develops around this orbit as it loses its stability; this behavior is still dominated by the LFV on decadal and multi-decadal time scales that is typical of oceanic processes. Atmospheric diagnostics also reveals the presence of predominant low- and high-pressure zones, as well as of a subtropical jet; these features recall realistic climatological properties of the oceanic atmosphere. Finally, a predictability analysis is performed. Once the decadal-scale periodic orbits develop, the coupled system’s short-term instabilities—as measured by its Lyapunov exponents—are drastically reduced, indicating the ocean’s stabilizing role on the atmospheric dynamics. On decadal time scales, the recurrence of the solution in a certain region of the invariant subspace associated with slow modes displays some extended predictability, as reflected by the oscillatory behavior of the error for the atmospheric variables at long lead times.


      PubDate: 2015-07-28T20:53:41Z
       
  • Dynamics and statistics of noise-like pulses in modelocked lasers
    • Abstract: Publication date: Available online 21 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Graham M. Donovan
      Noise-like pulses and optical rogue waves are connected nonlinear phenomena which can occur in passively modelocked laser systems. Here we consider a range of model systems to explore the conditions under which noise-like pulses can be expected to occur, and further when the resulting statistics meet the optical rogue wave criteria. We show, via a series of careful simulations, that noise-like pulses and optical rogue waves can arise either separately or together, and that they may emerge from standard soliton-like solutions via different mechanisms. We also propose a quantitative definition of noise-like pulses, and explore the issues in carefully convergence testing numerical methods for such systems.


      PubDate: 2015-07-25T10:32:40Z
       
  • Editorial Board
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307




      PubDate: 2015-07-25T10:32:40Z
       
  • Bandcount adding structure and collapse of chaotic attractors in a
           piecewise linear bimodal map
    • Abstract: Publication date: Available online 17 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Viktor Avrutin, Manuel Clüver, Vincent Mahout, Danièle Fournier-Prunaret
      In this work we investigate bifurcation structures in the chaotic domain of a piecewise linear bimodal map. The map represents a model of a circuit proposed to generate chaotic signals. For practical purposes it is necessary that the map generates robust broad-band chaos. However, experiments show that this requirement is fulfilled not everywhere. We show that the chaotic domain in the parameter space of this map contains regions in which the map has multi-band chaotic attractors. These regions are confined by bifurcation curves associated with homoclinic bifurcations of unstable cycles, and form a so-called bandcount adding structure previously reported to occur in discontinuous maps. Additionally, it is shown that inside each of these regions chaotic attractors collapse to particular cycles existing on a domain of zero measure in the parameter space and organized in a period adding structure in the form known for circle maps.


      PubDate: 2015-07-21T10:27:24Z
       
  • On discontinuous travelling wave solutions for a class of hyperbolic
           reaction-diffusion models
    • Abstract: Publication date: Available online 10 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): E. Barbera , C. Currò , G. Valenti
      A class of hyperbolic reaction-diffusion models is derived within the context of Extended Thermodynamics. This kind of models avoids the unphysical features concerning the instantaneous diffusive effects typical of parabolic equations and it results to be suitable for describing invasive phenomena with a well-defined boundary. Under suitable assumptions the non-existence of smooth travelling waves is proved within a region in the state-space. As an illustrative example of such a theoretical analysis, a model describing the infiltration of rain water in semi-arid environment is derived and both continuous and discontinuous travelling waves are investigated.


      PubDate: 2015-07-11T02:58:12Z
       
  • Thermoconvective instabilities to explain the main characteristics of a
           dust devil-like vortex
    • Abstract: Publication date: Available online 10 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): M.C. Navarro , D. Castaño , H. Herrero
      In this paper we show numerically that the main characteristics of a dust devil-like vortex: vertical vorticity generation, eye formation, and tilting of the eye/axis of rotation, can be explained by thermoconvective mechanisms. By considering a cylinder non-homogeneously heated from below we prove that an intense localized heating on the ground generates a convective stationary axisymmetric flow that begins to spiral up around a central axis when perturbation vertical vorticity is permitted and a critical vertical temperature gradient is exceeded, thus forming an axisymmetric vortex. If the intense heating on the ground is not too localized and the temperature gradient continues increasing, central downdrafts appear in the vortex and an eye is formed. We show that the axisymmetric vortex loses stability toward a new state for which the axisymmetry is broken, the axis of rotation or proper eye displaces from the center and tilts. The vortical states found are comparable to dust devils. These findings establish the relevance of thermoconvection on the formation and evolution of these atmospheric phenomena.


      PubDate: 2015-07-11T02:58:12Z
       
  • Equivalence of a compressible inviscid flow and the Bloch vector under the
           thermal Jaynes–Cummings model
    • Abstract: Publication date: Available online 9 July 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Hiroo Azuma , Masashi Ban
      In this paper, we show that the time evolution of the Bloch vector governed by the thermal Jaynes–Cummings model is equivalent to a compressible inviscid flow with zero vorticity. Because of its quasiperiodicity, the dynamics of the Bloch vector includes countably infinite angular momenta as integrals of motion. Moreover, to derive the Bloch vector, we trace out the Hilbert space of the cavity field and remove entanglement between the single atom and the cavity mode. These facts indicate that the dynamics of the Bloch vector can be described with a hidden-variable model that has local determinism and a countably infinite number of degrees of freedom. Our results fit these considerations.


      PubDate: 2015-07-11T02:58:12Z
       
  • O(2) Hopf bifurcation of viscous shock waves in a channel
    • Abstract: Publication date: 15 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 308
      Author(s): Alin Pogan , Jinghua Yao , Kevin Zumbrun
      Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O ( 2 ) transverse Hopf bifurcation, or “cellular instability”, of viscous shock waves in a channel, for a class of quasilinear hyperbolic–parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic–parabolic energy estimates, and (ii) handle O ( 2 ) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic–parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov–Schmidt reduction of the time- T map, yielding a four-dimensional problem with O ( 2 ) plus approximate S 1 symmetry, which we treat “by hand” using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.


      PubDate: 2015-07-11T02:58:12Z
       
  • Editorial Board
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306




      PubDate: 2015-07-11T02:58:12Z
       
  • Domain coarsening in a subdiffusive Allen–Cahn equation
    • Abstract: Publication date: Available online 26 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): M. Abu Hamed , A.A. Nepomnyashchy
      Domain coarsening in a one-dimensional bistable system governing by a subdiffusive generalization of the Allen–Cahn equation is considered. Integro-differential equations governing the motion of interacting domain walls are derived and solved analytically and numerically. The dependence of the domain wall dynamics on the subdiffusion parameter is investigated.


      PubDate: 2015-07-01T11:33:57Z
       
  • A multidomain model for ionic electrodiffusion and osmosis with an
           application to cortical spreading depression
    • Abstract: Publication date: Available online 29 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Yoichiro Mori
      Ionic electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of this model is that it satisfies a free energy identity, ensuring the thermodynamic consistency of the model. A numerical scheme is developed for the model in one spatial dimension and is applied to a model of cortical spreading depression, a propagating breakdown of ionic and cell volume homeostasis in the brain.


      PubDate: 2015-07-01T11:33:57Z
       
  • Transitions between streamline topologies of structurally stable
           Hamiltonian flows in multiply connected domains
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Takashi Sakajo , Tomoo Yokoyama
      We consider Hamiltonian vector fields with a dipole singularity satisfying the slip boundary condition in two-dimensional multiply connected domains. One example of such Hamiltonian vector fields is an incompressible and inviscid flow in exterior multiply connected domains with a uniform flow, whose Hamiltonian is called the stream function. Here, we are concerned with topological structures of the level sets of the Hamiltonian, which we call streamlines by analogy from incompressible fluid flows. Classification of structurally stable streamline patterns has been considered in Yokoyama and Sakajo (2013), where a procedure to assign a unique sequence of words, called the maximal word, to these patterns is proposed. Thanks to this procedure, we can identify every streamline pattern with its representing sequence of words up to topological equivalence. In the present paper, based on the theory of word representations, we propose a combinatorial method to provide a list of possible transient structurally unstable streamline patterns between two different structurally stable patterns by simply comparing their maximal word representations without specifying any Hamiltonian. Although this method cannot deal with topological streamline changes induced by bifurcations, it reveals the existence of many non-trivial global transitions in a generic sense. We also demonstrate how the present theory is applied to fluid flow problems with vortex structures.


      PubDate: 2015-06-26T14:28:59Z
       
  • Stability of front solutions in a model for a surfactant driven flow on an
           inclined plane
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Anna Ghazaryan , Stéphane Lafortune , Vahagn Manukian
      We consider a model for the flow of a thin liquid film down an inclined plane in the presence of a surfactant. The model is known to possess various families of traveling wave solutions. We use a combination of analytical and numerical methods to study the stability of the traveling waves. We show that for at least some of these waves the spectra of the linearization of the system about them are within the closed left-half complex plane.


      PubDate: 2015-06-26T14:28:59Z
       
  • Adaptive bipartite consensus on coopetition networks
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Jiangping Hu , Hong Zhu
      In this paper, a bipartite consensus tracking problem is considered for a group of autonomous agents on a coopetition network, on which the agents interact cooperatively and competitively simultaneously. The coopetition network involves positive and negative edges and is conveniently modeled by a signed graph. Additionally, the dynamics of all the agents are subjected to unknown disturbances, which are represented by linearly parameterized models. An adaptive estimation scheme is designed for each agent by virtue of the relative position measurements and the relative velocity measurements from its neighbors. Then a consensus tracking law is proposed for a new distributed system, which uses the relative measurements as the new state variables. The convergence of the consensus tracking error and the parameter estimation are analyzed even when the coopetition network is time-varying and no more global information about the bounds of the unknown disturbances is available to all the agents. Finally, some simulation results are provided to demonstrate the formation of the bipartite consensus on the coopetition network.


      PubDate: 2015-06-26T14:28:59Z
       
  • Traveling wave profiles for a crystalline front invading liquid states:
           Analytical and numerical solutions
    • Abstract: Publication date: 15 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 308
      Author(s): P.K. Galenko , F. Iunes Sanches , K.R. Elder
      The properties of a two dimensional crystalline phase invading a metastable or unstable liquid state are examined using the amplitude expansion formulation of the hyperbolic and parabolic phase-field crystal model. When the amplitudes are real and equal to each other, analytic expressions are derived for the profile of a steady state liquid–solid front traveling at constant velocity. Numerical simulations of the full amplitude formulation are conducted and compared with the analytic results. Close to the melting transition the analytic results for the liquid–solid profile, velocity and width are in quantitative agreement with the numerical results and disagree far from the transition.


      PubDate: 2015-06-26T14:28:59Z
       
  • Phase field based nonlocal anisotropic damage mechanics model
    • Abstract: Publication date: 15 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 308
      Author(s): Navid Mozaffari , George Z. Voyiadjis
      A nonlocal anisotropic damage theory is developed in this work through the phase field method to address the anisotropic damage evolution in materials. The anisotropic damage is discussed and appropriate nonconserved order parameters in three mutually perpendicular directions are defined to find the growth of the components of a second order diagonal damage tensor corresponding to the principal directions of a general second order damage tensor. In contrast to the previous models, two new tensors are proposed to act as interpolation and potential functions along with the Allen–Cahn equation in order to obtain the evolution of the order parameters, which is the basis of the definition of the damage rate. The tensor formulation of the growth of the components of the damage tensor is proposed for the first time. It is shown that, by introducing a set of material parameters including a length scale parameter due to damage, there is a robust and simplified way to model the nonlocal behavior of damage and predict the corresponding material behavior as components of a second order diagonal damage tensor.


      PubDate: 2015-06-26T14:28:59Z
       
  • Star pentagon and many stable choreographic solutions of the Newtonian
           4-body problem
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Tiancheng Ouyang , Zhifu Xie
      In this paper, we give a rigorous proof of the existence of infinitely many simple choreographic solutions in the classical Newtonian 4-body problem. These orbits are discovered by a variational method with structural prescribed boundary conditions (SPBC). This method provides an initial path that is obtained by minimizing the Lagrangian action functional over the SPBC. We prove that the initial path can be extended to a periodic or quasi-periodic solution. With computer-assistance, a family of choreographic orbits of this type is shown to be linearly stable. Among the many linearly stable simple choreographic orbits, the most extraordinary one is the stable star pentagon choreographic solution. We also prove the existence of infinitely many double choreographic periodic solutions, infinitely many non-choreographic periodic solutions and uncountably many quasi-periodic solutions. Each type of periodic solutions has many stable solutions and possibly infinitely many stable solutions. Our results with SPBC largely complement the current results by minimizing the action on a loop space.


      PubDate: 2015-06-26T14:28:59Z
       
  • Dynamics and absorption properties of stochastic equations with
           Hölder diffusion coefficients
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): Jonathan Touboul , Gilles Wainrib
      In this article, we characterize the dynamics and absorption properties of a class of stochastic differential equations around singular points where both the drift and diffusion functions vanish. According to the Hölder coefficient α of the diffusion function around the singular point, we identify different regimes: a regime where the solutions almost surely reach the singular point in finite time, and regimes of exponential attraction or repulsion from the singular point. Stability of the absorbing state, large deviations for the absorption time, existence of stationary or quasi-stationary distributions are discussed. In particular, we show that quasi-stationary distributions only exist for α < 3 / 4 , and for α ∈ ( 3 / 4 , 1 ) , no quasi-stationary distribution is found and numerical simulations tend to show that the process conditioned on not being absorbed initiates an almost sure exponential convergence towards the absorbing state (as is demonstrated to be true for α = 1 ). These results have several implications in the understanding of stochastic bifurcations, and we completely unfold two generic situations: the pitchfork and saddle–node bifurcations, and discuss the Hopf bifurcation in the appendix.


      PubDate: 2015-06-26T14:28:59Z
       
  • Two-dimensional expansion of a condensed dense Bose gas
    • Abstract: Publication date: 1 July 2015
      Source:Physica D: Nonlinear Phenomena, Volume 307
      Author(s): E.S. Annibale , A. Gammal , K. Ziegler
      We study the expansion dynamics of a condensate in a strongly interacting Bose gas in the presence of an obstacle. Our focus is on the generation of shock waves after the Bose gas has passed the obstacle. The strongly interacting Bose gas is described in the slave-boson representation. A saddle-point approximation provides a nonlinear equation of motion for the macroscopic wave function, analogous to the Gross–Pitaevskii equation of a weakly interacting Bose gas but with different nonlinearity. We compare the results with the Gross–Pitaevskii dynamics of a weakly interacting Bose gas and find a similar behavior with a slower behavior of the strongly interacting system.


      PubDate: 2015-06-26T14:28:59Z
       
  • Dynamical Hamiltonian–Hopf instabilities of periodic traveling waves
           in Klein–Gordon equations
    • Abstract: Publication date: Available online 25 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): R. Marangell , P.D. Miller
      We study the unstable spectrum close to the imaginary axis for the linearization of the nonlinear Klein–Gordon equation about a periodic traveling wave in a co-moving frame. We define dynamical Hamiltonian–Hopf instabilities as points in the stable spectrum that are accumulation points for unstable spectrum, and show how they can be determined from the knowledge of the discriminant of an associated Hill’s equation. This result allows us to give simple criteria for the existence of dynamical Hamiltonian–Hopf instabilities in terms of instability indices previously shown to be useful in stability analysis of periodic traveling waves. We also discuss how these methods can be applied to more general nonlinear wave equations.


      PubDate: 2015-06-26T14:28:59Z
       
  • On Slater’s criterion for the breakup of invariant curves
    • Abstract: Publication date: Available online 24 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): C.V. Abud , I.L. Caldas
      We numerically explore Slater’s theorem in the context of dynamical systems to study the breakup of invariant curves. Slater’s theorem states that an irrational translation over a circle returns to an arbitrary interval in at most three different recurrence times expressible by the continued fraction expansion of the related irrational number. The hypothesis considered in this paper is that Slater’s theorem can be also verified in the dynamics of invariant curves. Hence, we use Slater’s theorem to develop a qualitative and quantitative numerical approach to determine the breakup of invariant curves in the phase space of area-preserving maps.


      PubDate: 2015-06-26T14:28:59Z
       
  • Extreme phase sensitivity in systems with fractal isochrons
    • Abstract: Publication date: Available online 19 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): A. Mauroy , I. Mezić
      Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this context we report on the fractal properties of the isochrons of some continuous-time asymptotically periodic systems. We define a global measure of phase sensitivity that we call the phase sensitivity coefficient and show that it is an invariant of the system related to the capacity dimension of the isochrons. Similar results are also obtained with discrete-time systems. As an illustration of the framework, we compute the phase sensitivity coefficient for popular models of bursting neurons, suggesting that some elliptic bursting neurons are characterized by isochrons of high fractal dimensions and exhibit a very sensitive (unreliable) phase response.


      PubDate: 2015-06-26T14:28:59Z
       
  • Canalization and the stability of NK-Kauffman networks
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Federico Zertuche
      Boolean variables are such that they take values on Z 2 ≅ { 0 , 1 } . NK-Kauffman networks are dynamical deterministic systems of N Boolean functions that depend only on K ≤ N Boolean variables. They were proposed by Kauffman as a first step to understand cellular behavior (Kauffman, 1969) with great success. Among the problems that still have not been well understood in Kauffman networks, is the mechanism that regulates the phase transition of the system from an ordered phase where small changes of the initial state decay, to a chaotic one, where they grow exponentially. I show, that this mechanism is regulated through the irreducible decomposition of Boolean functions proposed in Zertuche (2009). This is in contrast to previous knowledge that attributed it to canalization. I also review other statistical properties of Kauffman networks that Boolean irreducibility explains.


      PubDate: 2015-06-26T14:28:59Z
       
  • Multistability and hidden attractors in a relay system with hysteresis
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Zhanybai T. Zhusubaliyev , Erik Mosekilde , Vasily G. Rubanov , Roman A. Nabokov
      For nonlinear dynamic systems with switching control, the concept of a “hidden attractor” naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations.


      PubDate: 2015-06-26T14:28:59Z
       
  • Partial classification of Lorenz knots: Syllable permutations of torus
           knots words
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Paulo Gomes , Nuno Franco , Luís Silva
      We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston’s theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.


      PubDate: 2015-06-26T14:28:59Z
       
  • Bifurcations and strange nonchaotic attractors in a phase oscillator model
           of glacial–interglacial cycles
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Takahito Mitsui , Michel Crucifix , Kazuyuki Aihara
      Glacial–interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is ∼ 40 kyr before the so-called middle Pleistocene transition between ∼ 1.2 and ∼ 0.7 Myr ago, and it is ∼ 100 kyr after the transition. In this paper, the dynamics of glacial–interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle–node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles is robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaotic attractor.


      PubDate: 2015-06-26T14:28:59Z
       
  • On the backward behavior of some dissipative evolution equations
    • Abstract: Publication date: 15 June 2015
      Source:Physica D: Nonlinear Phenomena, Volume 306
      Author(s): Yanqiu Guo , Edriss S. Titi
      We prove that every solution of a KdV–Burgers–Sivashinsky type equation blows up in the energy space, backward in time, provided the solution does not belong to the global attractor. This is a phenomenon contrast to the backward behavior of the periodic 2D Navier–Stokes equations studied by Constantin et al. (1997), but analogous to the backward behavior of the Kuramoto–Sivashinsky equation discovered by Kukavica and Malcok (2005). Also we study the backward behavior of solutions to the damped driven nonlinear Schrödinger equation, the complex Ginzburg–Landau equation, and the hyperviscous Navier–Stokes equations. In addition, we provide some physical interpretation of various backward behaviors of several perturbations of the KdV equation by studying explicit cnoidal wave solutions. Furthermore, we discuss the connection between the backward behavior and the energy spectra of the solutions. The study of backward behavior of dissipative evolution equations is motivated by the investigation of the Bardos–Tartar conjecture on the Navier–Stokes equations stated in Bardos and Tartar (1973).


      PubDate: 2015-06-26T14:28:59Z
       
  • Transport bounds for a truncated model of Rayleigh–Bénard
           convection
    • Abstract: Publication date: Available online 10 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Andre N. Souza , Charles R. Doering
      We investigate absolute limits on heat transport in a truncated model of Rayleigh–Bénard convection. Two complementary mathematical approaches—a background method analysis and an optimal control formulation—are used to derive upper bounds in a distinguished eight-ODE model proposed by Gluhovsky, Tong, and Agee. In the optimal control approach the flow no longer obeys an equation of motion, but is instead a control variable. Both methods produce the same estimate, but in contrast to the analogous result for the seminal three-ODE Lorenz system, the best upper bound apparently does not always correspond to an exact solution of the equations of motion.


      PubDate: 2015-06-26T14:28:59Z
       
  • On the motion of droplets driven by solutal Marangoni convection in alloy
           systems with a miscibility gap
    • Abstract: Publication date: Available online 9 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Fei Wang , Michael Selzer , Britta Nestler
      In the first part of this work, we analytically study the motion of two droplets driven by solutal Marangoni convection in a bipolar coordinate. Particular solutions for the Laplace and Stokes equations are found by applying Robin type boundary conditions for mass transfer and by utilizing continuity of stream function and impenetrability at the surface of droplets. The solutions for the Laplace and Stokes equations are connected by the tangential stress balance between the viscosity stress and the Marangoni stress caused by concentration gradients. In the second part, we numerically investigate the motion of two droplets in an immiscible fluid by solving the combined convective Cahn–Hilliard and Navier–Stokes equations, where the capillary tensor is used to account for the Marangoni force. A significant outcome of the present work is that the attraction or repulsion of droplets is determined by droplet radius and the Marangoni number. In both cases, we obtain the stream lines affected by the spacing between droplets and the ratio of the radius of the droplet.
      Graphical abstract image

      PubDate: 2015-06-26T14:28:59Z
       
  • Nonlinear conductance and heterogeneity of voltage-gated ion channels
           allow defining electrical surface domains in cell membranes
    • Abstract: Publication date: Available online 6 June 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Javier Cervera , José A. Manzanares , Salvador Mafe
      The membrane potential of a cell measured by typical electrophysiological methods is only an average magnitude and experimental techniques allowing a more detailed mapping of the cell surface have shown the existence of spatial domains with locally different electric potentials and currents. Electrical potentials in non-neural cells are regulated by the nonlinear conductance of membrane ion channels. Voltage-gated potassium channels participate in cell hyperpolarization/depolarization processes and control the electrical signals over the cell surface, constituting good candidates to study basic biological questions on a more simplified scale than the complex cell membrane. These channels show also a high heterogeneity, making it possible to analyze the effects of diversity in the electrical responses of channels localized on spatial domains. We use a phenomenological approach of voltage gating that reproduces the observed rectification characteristics of inward rectifying potassium channels and relate the threshold voltage heterogeneity of the channels to the establishment of spatial domains with different electrical sensitivities. Although our model is only a limited picture of the whole cell membrane, it shows that domains with different ion channels may permit or suppress steady state bioelectrical signals over the cell surface according to their particular voltage sensitivity. Also, the nonlinear electrical coupling of channels with different threshold potentials can lead to a rich variety of bioelectrical phenomena, including regions of membrane potential bi-stability.
      Graphical abstract image

      PubDate: 2015-06-26T14:28:59Z
       
 
 
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